Lesson 42c: PV Diagrams

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Lesson 42c: PV Diagrams"

Transcription

1 Lesson 42c: V Diagrams From the last section, you were probably wondering what happens when we do something like add heat to a sealed cylinder. This sounds like a pretty dangerous idea if you think back to the WHMIS training you had about compressed gas cylinders in Science 10. You might be thinking that it could make the cylinder explode because of an increase in pressure. These are the sorts of situations we can consider when we look at V diagrams. A V diagram is a graph of ressure as a function of Volume. ressure is measured in either ascals (a) or Newtons per metre squared. Volume is measured in metres cubed (m 3 ). There are four different situations that you can expect to see shown in V diagrams: 1. Isobaric: the gas is held at a constant pressure 2. Isochoric: the gas is held at a constant volume 3. Isothermal: the gas is held at a constant temperature 4. Adiabatic: No heat flows in or out of the gas Isobaric Isobaric is actually a pretty easy thing to show on a V diagram, and also pretty easy to understand from an example of a situation in which it is happening. Imagine that you have a cylinder filled with a gas. At the top is a movable piston that has a few kilograms mass. At the start the pressure is a certain amount for the volume of gas involved. We place a heat source under the cylinder and slowly heat it up. Since this is an isobaric process, the pressure must stay the same as it was at the start. We also expect that with the extra internal energy heat source Illustration 1: A cylinder of gas is heated so that it expands while keeping its pressure constant. the molecules have gained from the heat source, they will be bouncing around a bit more. This must result in the gas expanding in the cylinder! The gas will do work against the piston as it expands, where W = Fd. The force is caused by the pressure acting on the surface area of the piston, so we can use the formula... F = A F = force (N) = pressure (a = N/m 2 ) A = area of the piston (m 2 ) d heat source 5/5/2011 studyphysics.ca age 1 of 6 / C&J Section

2 We can substitute the two formulas together to get... W = Fd W = Ad W = - ΔV F = A Remember from math that volume can be calculated for a cylinder by taking the area of its end and multiplying it by the height. The distance the piston moved up in this example is like a change in height. This means that ΔV = Ad. The negative sign is added in the final formula on the A data sheet so we get the correct sign for W. This formula would let us calculate the work done by the gas on the piston as it expands. Example 1: A gas at 4.0e5 a is in a cylinder with a piston. During an isobaric process the gas is heated and expands from 0.25 m 3 to 0.55 m 3. Determine the work done by the gas on the cylinder, and sketch a V diagram of the situation. W = - ΔV W = - (V f V i ) W = - 4.0e5 ( ) W = -1.2e5 J The V diagram shows a gas going from a smaller to a bigger volume, while the pressure stays constant. Since the volume of the gas increased, we know work was done by the gas. The arrow has been added to show the way the process went from start to finish. If you look at how we calculated the work done, you might notice that it would have been the same answer if we had calculated the area under the graph. The area under the line on a V diagram is the work done! This is true for any V diagram, so keep it in mind. We can also realize something about the temperature change that must be happening if we use the ideal gas law. Since the pressure (), the amount of gas (n), and the gas constant (R) all stay constant... V = nrt V α T Illustration 2: An isobaric process where the gas does work. Volume (V) is directly related to temperature (T), so as the volume got bigger the temperature was also increasing. Duh, you say, we had already said we were heating the cylinder. The point is that the situation agrees with the physics. 5/5/2011 studyphysics.ca age 2 of 6 / C&J Section

3 Isochoric Let's take the previous idea of a gas in a cylinder and just change it a little bit. In an isochoric process the gas must keep a constant volume, so we will put the gas in a sealed container that can not change size or shape. As we heat it up more and more, the gas will want to expand even though it can't. This will result in an increase of pressure inside the cylinder. The increase in pressure will also create more force against the sides of the cylinder, but since nothing is moving, no work is done. W = Fd = F (0) = 0 J The first law of thermodynamics shows that since no work is being done (W = 0 J), all that heat being added just increases the internal energy. ΔU = Q + W ΔU = Q For the V diagram of the isochoric process we've been talking about, we get something like the diagram shown here. Notice how the volume stays the same while the pressure builds. Since it is a vertical line, there is no area under the line, which means no work is done (just like we figured out a moment ago). We can look at isochoric processes using the ideal gas law also. Now the volume (V) stays constant, along with the amount of gas (n), and the gas constant (R)... V = nrt α T This shows us that the pressure is directly related to the temperature. So, as the temperature increased while we heated the cylinder, the pressure increased as well. Isothermal Isothermal examples are quite different from the last two, since the temperature remains constant. For the example we'll discuss here, we'll try to keep as much of the other ideas the same as possible. Imagine a cylinder with a piston on top that is filled with a gas. The cylinder is sitting inside a large container filled with water. If anything happens to the cylinder that would normally cause a temperature change in the gas, the water will either absorb or release heat to keep the gas in the cylinder at a constant temperature. We have been holding down on the piston a bit, but now we release it so that the piston rises. heat source Illustration 3: Volume stays constant during an isochoric process. Illustration 4: An isochoric process where no work is done. Illustration 5: An isothermal process with a cylinder in a large container of water. 5/5/2011 studyphysics.ca age 3 of 6 / C&J Section

4 The volume of the gas is expanding, and the pressure inside will be dropping. This is quite different from the other two processes, where one of these stayed constant. Work is being done by the gas (work is negative), so to keep the internal energy (and temperature) constant, the gas must be absorbing heat from the water. As long as the energy lost (by the gas doing work) equals the heat gained from the water, the internal energy will not change and the temperature stays the same. U =Q W but Q = - W so... U = W W U =0 The V diagram we get shows a curved line as the pressure and volume both change. The line is called an isotherm, because the temperature stayed the same. The isotherm is a curve. This happens because when the piston was being released there was a sudden drop in pressure as the gas expanded. As the process continued the pressure dropped more slowly as the volume increased. The area under the curve is still the work done. Since it is a curve, the only way to accurately find the area is to use calculus. You are not required to know how to do this. Just state the area under the line is the work done and you'll be fine. The internal energy change of zero (ΔU = 0) will be true as long as we start and finish on the same isotherm on the V diagram. Adiabatic During an adiabatic process no heat is added to the system. This is often confused with isothermal processes, since it is assumed that no heat exchange means the temperature stays constant. This is not true!!! Think of the isothermal process we just looked at. If we did not allow heat to enter from the water the temperature would have changed (it would have decreased). During an adiabatic process the heat transfer is zero, so Q = 0 J. This could happen in a situation where the cylinder is surrounded by an insulating material. According to the first law of thermodynamics, this means... U =Q W U =0 W U =W Illustration 6: During an isothermal process the pressure and volume both change, while the temperature stays the same. Illustration 7: An adiabatic process happens in an insulating material so heat can not be transfered. so the change in the internal energy is equal to the work done on or by the gas. If the gas is compressed (work done on the gas is positive) the internal energy increases. If the gas expands (work done by the gas is negative) the internal energy decreases. 5/5/2011 studyphysics.ca age 4 of 6 / C&J Section

5 The V diagram for an adiabatic process show a special result. An adiabatic process looks very much like an isothermal process, but it drops off to a lower point. This means it is on a different isotherm. Remember, isotherms are just lines that show where the temperature stays constant. As we've already discussed, in the adiabatic process where a gas expands, the work done by the gas causes the internal energy to decrease, so the temperature must decrease as well. This is why we drop to a lower isotherm. We can use a formula for calculating the internal energy of a system based on its temperature to do many problems, but it is especially helpful in adiabatic processes. Since ΔU = W for an adiabatic process, if we figure out the initial and final internal energies, we can figure out the work done on or by the gas without having to use calculus to figure out the area under the V curve. The internal energy is calculated using the formula U = 3 2 nrt U = internal energy (J) n = number of moles of gas (mol) R = gas constant T = temperature (K) Example 2: A well insulated cylinder with a piston contains 3.00 mol of gas at 525 K. If it goes through adiabatic expansion and ends at a temperature of 300 K, determine how much work the gas did. The V diagram we would get for this adiabatic process is shown here. Notice how we started on the 525 K isotherm, but ended on the 300 K isotherm. The temperature did not stay constant, so this process must be adiabatic. First we calculate the initial internal energy of the gas... U i = 3 2 nrt U i = U i = J and then the final internal energy... U f = 3 2 nrt U f = U f = J Illustration 8: During an adiabatic process the temperature changes, so we end up on a different isotherm. adiabatic process 300 K isotherm isothermal process 525 K isotherm 5/5/2011 studyphysics.ca age 5 of 6 / C&J Section

6 Now we can use ΔU = W to figure out how much work the gas did... U =U f U i U = U =W = = 8.41e3 J This means that the gas did 8.41e3 J of work to expand. Summary Of rocesses rocess Constant V Diagram Ideal Gas Law First Law of Thermodynamics Isobaric ressure Horizontal line V α T ΔU = Q + W Isochoric Volume Vertical line α T ΔU = Q Isothermal Temperature Curved line V α T ΔU = 0 Adiabatic No heat exchanged Curved line (jumps to different isotherm) V = nrt (only nr are constant) ΔU = W 5/5/2011 studyphysics.ca age 6 of 6 / C&J Section

Expansion and Compression of a Gas

Expansion and Compression of a Gas Physics 6B - Winter 2011 Homework 4 Solutions Expansion and Compression of a Gas In an adiabatic process, there is no heat transferred to or from the system i.e. dq = 0. The first law of thermodynamics

More information

Chapter 15: Thermodynamics

Chapter 15: Thermodynamics Chapter 15: Thermodynamics The First Law of Thermodynamics Thermodynamic Processes (isobaric, isochoric, isothermal, adiabatic) Reversible and Irreversible Processes Heat Engines Refrigerators and Heat

More information

Heat and Work. First Law of Thermodynamics 9.1. Heat is a form of energy. Calorimetry. Work. First Law of Thermodynamics.

Heat and Work. First Law of Thermodynamics 9.1. Heat is a form of energy. Calorimetry. Work. First Law of Thermodynamics. Heat and First Law of Thermodynamics 9. Heat Heat and Thermodynamic rocesses Thermodynamics is the science of heat and work Heat is a form of energy Calorimetry Mechanical equivalent of heat Mechanical

More information

PSS 17.1: The Bermuda Triangle

PSS 17.1: The Bermuda Triangle Assignment 6 Consider 6.0 g of helium at 40_C in the form of a cube 40 cm. on each side. Suppose 2000 J of energy are transferred to this gas. (i) Determine the final pressure if the process is at constant

More information

Lecture 6: Intro to Entropy

Lecture 6: Intro to Entropy Lecture 6: Intro to Entropy Reading: Zumdahl 0., 0., 0.3 Outline: Why enthalpy isn t enough. Statistical interpretation of entropy Boltzmann s Formula Heat engine leads to Entropy as a state function Problems:Z0.-4,

More information

HEAT UNIT 1.1 KINETIC THEORY OF GASES. 1.1.1 Introduction. 1.1.2 Postulates of Kinetic Theory of Gases

HEAT UNIT 1.1 KINETIC THEORY OF GASES. 1.1.1 Introduction. 1.1.2 Postulates of Kinetic Theory of Gases UNIT HEAT. KINETIC THEORY OF GASES.. Introduction Molecules have a diameter of the order of Å and the distance between them in a gas is 0 Å while the interaction distance in solids is very small. R. Clausius

More information

c. Applying the first law of thermodynamics from Equation 15.1, we find that c h c h.

c. Applying the first law of thermodynamics from Equation 15.1, we find that c h c h. Week 11 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution

More information

Problem Set 3 Solutions

Problem Set 3 Solutions Chemistry 360 Dr Jean M Standard Problem Set 3 Solutions 1 (a) One mole of an ideal gas at 98 K is expanded reversibly and isothermally from 10 L to 10 L Determine the amount of work in Joules We start

More information

Thermodynamics AP Physics B. Multiple Choice Questions

Thermodynamics AP Physics B. Multiple Choice Questions Thermodynamics AP Physics B Name Multiple Choice Questions 1. What is the name of the following statement: When two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium

More information

Physics 2101 Section 3 April 26th: Chap. 18 : Chap Ann n ce n e t nnt : Exam #4, April Exam #4,

Physics 2101 Section 3 April 26th: Chap. 18 : Chap Ann n ce n e t nnt : Exam #4, April Exam #4, Physics 2101 Section 3 April 26 th : Chap. 18-1919 Announcements: n nt Exam #4, April 28 th (Ch. 13.6-18.8) 18.8) Final Exam: May 11 th (Tuesday), 7:30 AM Make up Final: May 15 th (Saturday) 7:30 AM Class

More information

Thermodynamics Answers to Tutorial # 1

Thermodynamics Answers to Tutorial # 1 Thermodynamics Answers to Tutorial # 1 1. (I) Work done in free expansion is Zero as P ex = 0 (II) Irreversible expansion against constant external pressure w = P ex (V 2 V 1 ) V 2 = nrt P 2 V 1 = nrt

More information

Example 1. Solution: Diagram: Given: m = 1 kg P 1 = P 2 = 0.8 MPa = constant v 1 = m 3 /kg v 2 = m 3 /kg. Find:

Example 1. Solution: Diagram: Given: m = 1 kg P 1 = P 2 = 0.8 MPa = constant v 1 = m 3 /kg v 2 = m 3 /kg. Find: Example 1 Problem Statement: A piston/cylinder device contains one kilogram of a substance at 0.8 MPa with a specific volume of 0.2608 m 3 /kg. The substance undergoes an isobaric process until its specific

More information

Ideal Gases and the First Law of Thermodynamics

Ideal Gases and the First Law of Thermodynamics N.1 - Ideal Gases Chapter N Ideal Gases and the First Law of Thermodynamics linn College - hysics 45 - Terry Honan asic Definitions The assumption behind an ideal gas is that it is a collection of non-interacting

More information

Problems of Chapter 2

Problems of Chapter 2 Section 2.1 Heat and Internal Energy Problems of Chapter 2 1- On his honeymoon James Joule traveled from England to Switzerland. He attempted to verify his idea of the interconvertibility of mechanical

More information

Phys 2101 Gabriela González

Phys 2101 Gabriela González Phys 2101 Gabriela González If volume is constant ( isochoric process), W=0, and Tp -1 is constant. pv=nrt If temperature is constant ( isothermal process), ΔE int =0, and pv is constant. If pressure is

More information

The Ideal Gas law. I. Pressure

The Ideal Gas law. I. Pressure The Ideal Gas law I. Pressure A cylinder contains an ideal gas that is at room temperature. The cylinder is sealed with a piston of mass M and cross sectional area A that is free to move up and down without

More information

Answer, Key Homework 6 David McIntyre 1

Answer, Key Homework 6 David McIntyre 1 Answer, Key Homework 6 David McIntyre 1 This print-out should have 0 questions, check that it is complete. Multiple-choice questions may continue on the next column or page: find all choices before making

More information

THE KINETIC THEORY OF GASES

THE KINETIC THEORY OF GASES Chapter 19: THE KINETIC THEORY OF GASES 1. Evidence that a gas consists mostly of empty space is the fact that: A. the density of a gas becomes much greater when it is liquefied B. gases exert pressure

More information

Phys222 W11 Quiz 1: Chapters 19-21 Keys. Name:

Phys222 W11 Quiz 1: Chapters 19-21 Keys. Name: Name:. In order for two objects to have the same temperature, they must a. be in thermal equilibrium.

More information

Laws of Thermodynamics

Laws of Thermodynamics Laws of Thermodynamics Thermodynamics Thermodynamics is the study of the effects of work, heat, and energy on a system Thermodynamics is only concerned with macroscopic (large-scale) changes and observations

More information

The First Law of Thermodynamics

The First Law of Thermodynamics Thermodynamics The First Law of Thermodynamics Thermodynamic Processes (isobaric, isochoric, isothermal, adiabatic) Reversible and Irreversible Processes Heat Engines Refrigerators and Heat Pumps The Carnot

More information

Second Law of Thermodynamics

Second Law of Thermodynamics Thermodynamics T8 Second Law of Thermodynamics Learning Goal: To understand the implications of the second law of thermodynamics. The second law of thermodynamics explains the direction in which the thermodynamic

More information

Heat as Energy Transfer. Heat is energy transferred from one object to another because of a difference in temperature

Heat as Energy Transfer. Heat is energy transferred from one object to another because of a difference in temperature Unit of heat: calorie (cal) Heat as Energy Transfer Heat is energy transferred from one object to another because of a difference in temperature 1 cal is the amount of heat necessary to raise the temperature

More information

Lesson 40: Conservation of Energy

Lesson 40: Conservation of Energy Lesson 40: Conservation of Energy A large number of questions you will do involve the total mechanical energy. As pointed out earlier, the mechanical energy is just the total of all types of energy. In

More information

Lesson 10: Electric Fields

Lesson 10: Electric Fields Lesson 10: Electric Fields Just like the force due to gravity, the force due to electric charges can act over great distances. Keep in mind that most forces we deal with in everyday life are not like this.

More information

1. (10) Argon, Ar, exists at T = K, P = 4.87 MPa. Find its specific volume via

1. (10) Argon, Ar, exists at T = K, P = 4.87 MPa. Find its specific volume via NAME: SOLUTION AME 03 Thermodynamics Examination Profs. A. M. Ardekani and J. M. Powers 4 February 0. (0) Argon, Ar, exists at T = 65.9 K, P = 4.87 MPa. Find its specific volume via (a) the ideal gas law,

More information

More Kinetic Theory of Gases

More Kinetic Theory of Gases More Kinetic Theory of Gases Physics 1425 Lecture 32 Michael Fowler, UVa Vapor Pressure and Humidity The H 2 O molecules in liquid water strongly attract each other, holding the liquid together. But these

More information

Physics Final Exam Chapter 13 Review

Physics Final Exam Chapter 13 Review Physics 1401 - Final Exam Chapter 13 Review 11. The coefficient of linear expansion of steel is 12 10 6 /C. A railroad track is made of individual rails of steel 1.0 km in length. By what length would

More information

Thermodynamic Systems

Thermodynamic Systems Student Academic Learning Services Page 1 of 18 Thermodynamic Systems And Performance Measurement Contents Thermodynamic Systems... 2 Defining the System... 2 The First Law... 2 Thermodynamic Efficiency...

More information

ENTROPY AND THE SECOND LAW OF THERMODYNAMICS

ENTROPY AND THE SECOND LAW OF THERMODYNAMICS Chapter 20: ENTROPY AND THE SECOND LAW OF THERMODYNAMICS 1. In a reversible process the system: A. is always close to equilibrium states B. is close to equilibrium states only at the beginning and end

More information

Thermodynamics is the study of heat. It s what comes into play when you drop an ice cube

Thermodynamics is the study of heat. It s what comes into play when you drop an ice cube Chapter 12 You re Getting Warm: Thermodynamics In This Chapter Converting between temperature scales Working with linear expansion Calculating volume expansion Using heat capacities Understanding latent

More information

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 7 Ideal Gas Laws, Different Processes Let us continue

More information

Lesson 26: Reflection & Mirror Diagrams

Lesson 26: Reflection & Mirror Diagrams Lesson 26: Reflection & Mirror Diagrams The Law of Reflection There is nothing really mysterious about reflection, but some people try to make it more difficult than it really is. All EMR will reflect

More information

Chapter 19 Thermodynamics

Chapter 19 Thermodynamics 19.1 Introduction Chapter 19 Thermodynamics We can express the fundamental laws of the universe which correspond to the two fundamental laws of the mechanical theory of heat in the following simple form.

More information

Basic problems for ideal gases and problems to the first law of thermodynamics and cycles

Basic problems for ideal gases and problems to the first law of thermodynamics and cycles Basic problems for ideal gases and problems to the first law of thermodynamics and cycles SHORT SUMMARY OF THE FORMS: Equation of ideal gases: Number of moles: Universal gas constant: General gas equation

More information

Physics Assignment No 2 Chapter 20 The First Law of Thermodynamics Note: Answers are provided only to numerical problems.

Physics Assignment No 2 Chapter 20 The First Law of Thermodynamics Note: Answers are provided only to numerical problems. Serway/Jewett: PSE 8e Problems Set Ch. 20-1 Physics 2326 - Assignment No 2 Chapter 20 The First Law of Thermodynamics Note: Answers are provided only to numerical problems. 1. How long would it take a

More information

A Survey of Thermodynamics

A Survey of Thermodynamics A Survey of Thermodynamics Objective In this lab various topics relating to the study of thermodynamics will be explored. First, the flow of heat will be examined. Here an ice cube will be placed in a

More information

Problem Set 4 Solutions

Problem Set 4 Solutions Chemistry 360 Dr Jean M Standard Problem Set 4 Solutions 1 Two moles of an ideal gas are compressed isothermally and reversibly at 98 K from 1 atm to 00 atm Calculate q, w, ΔU, and ΔH For an isothermal

More information

HW#13a Note: numbers used in solution steps are different from your WebAssign values. Page 1 of 8

HW#13a Note: numbers used in solution steps are different from your WebAssign values. Page 1 of 8 Note: numbers used in solution steps are different from your WebAssign values. Page 1 of 8 Note: numbers used in solution steps are different from your WebAssign values. 1. Walker3 17.P.003. [565748] Show

More information

FUNDAMENTALS OF ENGINEERING THERMODYNAMICS

FUNDAMENTALS OF ENGINEERING THERMODYNAMICS FUNDAMENTALS OF ENGINEERING THERMODYNAMICS System: Quantity of matter (constant mass) or region in space (constant volume) chosen for study. Closed system: Can exchange energy but not mass; mass is constant

More information

Lesson 8: Velocity. Displacement & Time

Lesson 8: Velocity. Displacement & Time Lesson 8: Velocity Two branches in physics examine the motion of objects: Kinematics: describes the motion of objects, without looking at the cause of the motion (kinematics is the first unit of Physics

More information

From the equation (18-6) of textbook, we have the Maxwell distribution of speeds as: v 2 e 1 mv 2. 2 kt. 2 4kT m. v p = and f(2vp) as: f(v p ) = 1

From the equation (18-6) of textbook, we have the Maxwell distribution of speeds as: v 2 e 1 mv 2. 2 kt. 2 4kT m. v p = and f(2vp) as: f(v p ) = 1 Solution Set 9 1 Maxwell-Boltzmann distribution From the equation 18-6 of textbook, we have the Maxwell distribution of speeds as: fv 4πN In example 18-5, the most probable speed v p is given as m v e

More information

Energy in Thermal Processes: The First Law of Thermodynamics

Energy in Thermal Processes: The First Law of Thermodynamics Energy in Thermal Processes: The First Law of Thermodynamics 1. An insulated container half full of room temperature water is shaken vigorously for two minutes. What happens to the temperature of the water?

More information

Entropy and The Second Law of Thermodynamics

Entropy and The Second Law of Thermodynamics The Second Law of Thermodynamics (SL) Entropy and The Second Law of Thermodynamics Explain and manipulate the second law State and illustrate by example the second law of thermodynamics Write both the

More information

AP2 Thermal Physics. Answer: C

AP2 Thermal Physics. Answer: C A canister of pressurized nitrogen gas at room temperature is cooled in a freezer. More nitrogen gas at room temperature is pumped into the canister until the canister returns to its initial pressure.

More information

The Stirling Engine. Gunther Cronenberg. March 28, written in addition to the Stirling Lab at Uppsala University in February 2005

The Stirling Engine. Gunther Cronenberg. March 28, written in addition to the Stirling Lab at Uppsala University in February 2005 The Stirling Engine Gunther Cronenberg March 28, 2005 written in addition to the Stirling Lab at Uppsala University in February 2005 1 Contents 1 Introduction 3 2 History 3 3 Applications and Advantages

More information

Chapter 10 Temperature and Heat

Chapter 10 Temperature and Heat Chapter 10 Temperature and Heat What are temperature and heat? Are they the same? What causes heat? What Is Temperature? How do we measure temperature? What are we actually measuring? Temperature and Its

More information

The Equipartition Theorem

The Equipartition Theorem The Equipartition Theorem Degrees of freedom are associated with the kinetic energy of translations, rotation, vibration and the potential energy of vibrations. A result from classical statistical mechanics

More information

Absorption of Heat. Internal energy is the appropriate energy variable to use at constant volume

Absorption of Heat. Internal energy is the appropriate energy variable to use at constant volume 6 Absorption of Heat According to the First Law, E = q + w = q - P V, assuming P-V work is the only kind that can occur. Therefore, E = q V. The subscript means that the process occurs at constant volume.

More information

Lesson 39: Kinetic Energy & Potential Energy

Lesson 39: Kinetic Energy & Potential Energy Lesson 39: Kinetic Energy & Potential Energy Total Mechanical Energy We sometimes call the total energy of an object (potential and kinetic) the total mechanical energy of an object. Mechanical energy

More information

Ideal Gas Law Introduction Lesson Plan Keith Newman Chemistry 511 Final Project 2006/2007

Ideal Gas Law Introduction Lesson Plan Keith Newman Chemistry 511 Final Project 2006/2007 Ideal Gas Law Introduction Lesson Plan Keith Newman Chemistry 511 Final Project 2006/2007 Objectives: Students will be able to solve ideal gas law problems using algebraic ratios. Students will be able

More information

Chapter 19 First Law of Thermodynamics

Chapter 19 First Law of Thermodynamics Chapter 9 First Law o Thermodynamics When two bodies at dierent temperatures (T and T ) are placed in thermal contact, they ultimately reach a common temperature (T ) somewhere between the two initial

More information

Section P.9 Notes Page 1 P.9 Linear Inequalities and Absolute Value Inequalities

Section P.9 Notes Page 1 P.9 Linear Inequalities and Absolute Value Inequalities Section P.9 Notes Page P.9 Linear Inequalities and Absolute Value Inequalities Sometimes the answer to certain math problems is not just a single answer. Sometimes a range of answers might be the answer.

More information

Let s do the math: Escape Velocity

Let s do the math: Escape Velocity Let s do the math: Escape Velocity By Tim Farage The University of Texas at Dallas Well, time to have a little bit of fun with math and physics. You did a simulation to try to figure out what the escape

More information

Esystem = 0 = Ein Eout

Esystem = 0 = Ein Eout AGENDA: I. Introduction to Thermodynamics II. First Law Efficiency III. Second Law Efficiency IV. Property Diagrams and Power Cycles V. Additional Material, Terms, and Variables VI. Practice Problems I.

More information

Chapter 18 Temperature, Heat, and the First Law of Thermodynamics. Problems: 8, 11, 13, 17, 21, 27, 29, 37, 39, 41, 47, 51, 57

Chapter 18 Temperature, Heat, and the First Law of Thermodynamics. Problems: 8, 11, 13, 17, 21, 27, 29, 37, 39, 41, 47, 51, 57 Chapter 18 Temperature, Heat, and the First Law of Thermodynamics Problems: 8, 11, 13, 17, 21, 27, 29, 37, 39, 41, 47, 51, 57 Thermodynamics study and application of thermal energy temperature quantity

More information

Page 1. Set of values that describe the current condition of a system, usually in equilibrium. What is a state?

Page 1. Set of values that describe the current condition of a system, usually in equilibrium. What is a state? What is a state? Set of values that describe the current condition of a system, usually in equilibrium Is this physics different than what we have learned? Why do we learn it? How do we make the connection

More information

Reversible & Irreversible Processes

Reversible & Irreversible Processes Reversible & Irreversible Processes Example of a Reversible Process: Cylinder must be pulled or pushed slowly enough (quasistatically) that the system remains in thermal equilibrium (isothermal). Change

More information

Name Date Class THERMOCHEMISTRY. SECTION 17.1 THE FLOW OF ENERGY HEAT AND WORK (pages 505 510)

Name Date Class THERMOCHEMISTRY. SECTION 17.1 THE FLOW OF ENERGY HEAT AND WORK (pages 505 510) 17 THERMOCHEMISTRY SECTION 17.1 THE FLOW OF ENERGY HEAT AND WORK (pages 505 510) This section explains the relationship between energy and heat, and distinguishes between heat capacity and specific heat.

More information

Esystem = 0 = Ein Eout

Esystem = 0 = Ein Eout AGENDA: I. Introduction to Thermodynamics II. First Law Efficiency III. Second Law Efficiency IV. Property Diagrams and Power Cycles V. Additional Material, Terms, and Variables VI. Practice Problems I.

More information

Calculus Vocabulary without the Technical Mumbo Jumbo

Calculus Vocabulary without the Technical Mumbo Jumbo Calculus Vocabulary without the Technical Mumbo Jumbo Limits and Continuity By: Markis Gardner Table of Contents Average Rate of Change... 4 Average Speed... 5 Connected Graph... 6 Continuity at a point...

More information

Lecture 3: State Functions

Lecture 3: State Functions Lecture 3: State Functions Reading: Zumdahl 9.3, 9.4 Outline Example of Thermo. Pathways State Functions (9.4 for laboratory) Problems: (Z9.72,Z9.84),(Z9.29,Z9.30),(Z9.32,Z9.38) Z9.13 (Find the mistake)

More information

1.4 Exponential and logarithm graphs.

1.4 Exponential and logarithm graphs. 1.4 Exponential and logarithm graphs. Example 1. Recall that b = 2 a if and only if a = log 2 (b) That tells us that the functions f(x) = 2 x and g(x) = log 2 (x) are inverse functions. It also tells us

More information

Define the notations you are using properly. Present your arguments in details. Good luck!

Define the notations you are using properly. Present your arguments in details. Good luck! Umeå Universitet, Fysik Vitaly Bychkov Prov i fysik, Thermodynamics, 0-0-4, kl 9.00-5.00 jälpmedel: Students may use any book(s) including the textbook Thermal physics. Minor notes in the books are also

More information

Definition of Enthalpy

Definition of Enthalpy Lecture 2: Enthalpy Reading: Zumdahl 9.2, 9. Outline Definition of Enthalpy (ΔH) Definition of Molar Heat Capacity (C v and C p ) Calculating using C v and C p Changes in ΔE and ΔH as well as q and w for

More information

Refrigeration and Air-Conditioning Prof. M. Ramgopal Department of Mechanical Engineering Indian Institute of Technology, Kharagpur. Lecture No.

Refrigeration and Air-Conditioning Prof. M. Ramgopal Department of Mechanical Engineering Indian Institute of Technology, Kharagpur. Lecture No. Refrigeration and Air-Conditioning Prof. M. Ramgopal Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture No. # 16 Vapour Absorption Refrigeration systems (contd.) Welcome

More information

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 1 Introduction & Some Definitions Good afternoon everybody.

More information

Kinetic Theory of Gases A2 level notes LOJ

Kinetic Theory of Gases A2 level notes LOJ Data Sheet Extract The theory for ideal gases makes the following assumptions: The gas consists of very small atoms or molecules (spoken of as particles), each of which has an identical mass and are perfectly

More information

THERMODYNAMIC PROPERTIES AND CALCULATION. Academic Resource Center

THERMODYNAMIC PROPERTIES AND CALCULATION. Academic Resource Center THERMODYNAMIC PROPERTIES AND CALCULATION Academic Resource Center THERMODYNAMIC PROPERTIES A quantity which is either an attribute of an entire system or is a function of position which is continuous and

More information

Test Bank - Chapter 5 Multiple Choice

Test Bank - Chapter 5 Multiple Choice Test Bank - Chapter 5 The questions in the test bank cover the concepts from the lessons in Chapter 5. Select questions from any of the categories that match the content you covered with students. The

More information

AP Physics B Free Response Solutions

AP Physics B Free Response Solutions AP Physics B Free Response Solutions. (0 points) A sailboat at rest on a calm lake has its anchor dropped a distance of 4.0 m below the surface of the water. The anchor is suspended by a rope of negligible

More information

The First Law of Thermodynamics

The First Law of Thermodynamics The First Law of Thermodynamics (FL) The First Law of Thermodynamics Explain and manipulate the first law Write the integral and differential forms of the first law Describe the physical meaning of each

More information

MATHEMATICAL NOTES #1 - DEMAND AND SUPPLY CURVES -

MATHEMATICAL NOTES #1 - DEMAND AND SUPPLY CURVES - MATHEMATICAL NOTES #1 - DEMAND AND SUPPLY CURVES - Linear Equations & Graphs Remember that we defined demand as the quantity of a good consumers are willing and able to buy at a particular price. Notice

More information

Final Exam Review Questions PHY Final Chapters

Final Exam Review Questions PHY Final Chapters Final Exam Review Questions PHY 2425 - Final Chapters Section: 17 1 Topic: Thermal Equilibrium and Temperature Type: Numerical 12 A temperature of 14ºF is equivalent to A) 10ºC B) 7.77ºC C) 25.5ºC D) 26.7ºC

More information

CHM Kinetic Theory of Gases (r14) Charles Taylor 1/6

CHM Kinetic Theory of Gases (r14) Charles Taylor 1/6 CHM 110 - Kinetic Theory of Gases (r14) - 2014 Charles Taylor 1/6 Introduction We've talked about the gas laws and how they were derived from experiment. As scientists, we would like to figure out why

More information

LAB 15: HEAT ENGINES AND

LAB 15: HEAT ENGINES AND 251 Name Date Partners LAB 15: HEAT ENGINES AND THE FIRST LAW OF THERMODYNAMICS... the quantity of heat produced by the friction of bodies, whether solid or liquid, is always proportional to the quantity

More information

Advanced Algebra II: Activities and Homework. By: Kenny M. Felder

Advanced Algebra II: Activities and Homework. By: Kenny M. Felder Advanced Algebra II: Activities and Homework By: Kenny M. Felder Advanced Algebra II: Activities and Homework By: Kenny M. Felder Online: < http://cnx.org/content/col10686/1.5/ > C O N N E X I O N S Rice

More information

Research question: How does the velocity of the balloon depend on how much air is pumped into the balloon?

Research question: How does the velocity of the balloon depend on how much air is pumped into the balloon? Katie Chang 3A For this balloon rocket experiment, we learned how to plan a controlled experiment that also deepened our understanding of the concepts of acceleration and force on an object. My partner

More information

AP Physics Course 1 Summer Assignment. Teachers: Mr. Finn, Mrs. Kelly, Mr. Simowitz, Mr. Slesinski

AP Physics Course 1 Summer Assignment. Teachers: Mr. Finn, Mrs. Kelly, Mr. Simowitz, Mr. Slesinski AP Physics Course 1 Summer Assignment Teachers: Mr. Finn, Mrs. Kelly, Mr. Simowitz, Mr. Slesinski On the following pages, there are six sections that use the basic skills that will be used throughout the

More information

Gauss s Law for Gravity

Gauss s Law for Gravity Gauss s Law for Gravity D.G. impson, Ph.D. Department of Physical ciences and Engineering Prince George s Community College December 6, 2006 Newton s Law of Gravity Newton s law of gravity gives the force

More information

Surface Area of Irregular Solids

Surface Area of Irregular Solids CHAPTER 11 D Surface Area of Irregular Solids You will need a calculator c GOAL Calculate surface area and lateral area of figures created by combining right prisms, right pyramids, and right cylinders.

More information

Chapter 1 Rotational dynamics 1.1 Angular acceleration

Chapter 1 Rotational dynamics 1.1 Angular acceleration Chapter 1 Rotational dynamics 1.1 Angular acceleration Learning objectives: What do we mean by angular acceleration? How can we calculate the angular acceleration of a rotating object when it speeds up

More information

BLOSSOMS MODULE ARE RANDOM TRIANGLES ACUTE OR OBTUSE? By Gilbert Strang Professor of Mathematics Massachusetts Institute of Technology

BLOSSOMS MODULE ARE RANDOM TRIANGLES ACUTE OR OBTUSE? By Gilbert Strang Professor of Mathematics Massachusetts Institute of Technology BLOSSOMS MODULE ARE RANDOM TRIANGLES ACUTE OR OBTUSE? By Gilbert Strang Professor of Mathematics Massachusetts Institute of Technology Hi! I m Gilbert Strang. I teach math at MIT. Mostly what I teach is

More information

Calculating Work. Thermodynamics. Isobaric Process. Isochoric (isovolumetric) Work from Graph: Example 1 2/27/2012. Chapter 15

Calculating Work. Thermodynamics. Isobaric Process. Isochoric (isovolumetric) Work from Graph: Example 1 2/27/2012. Chapter 15 Pressure (X105 N/m2) Pressure (X105 N/m2) 2/27/2012 Thermodynamics Chapter 15 Calculating Work Work = area under Pressure vs. Volume graph W = Fd F = PA W=PAd W = P V Calculus link V 2 W = - p dv V 1 Isochoric

More information

Thermodynamics: First Law, Calorimetry, Enthalpy. Calorimetry. Calorimetry: constant volume. Monday, January 23 CHEM 102H T.

Thermodynamics: First Law, Calorimetry, Enthalpy. Calorimetry. Calorimetry: constant volume. Monday, January 23 CHEM 102H T. Thermodynamics: First Law, Calorimetry, Enthalpy Monday, January 23 CHEM 102H T. Hughbanks Calorimetry Reactions are usually done at either constant V (in a closed container) or constant P (open to the

More information

Section 7. Laws of Thermodynamics: Too Hot, Too Cold, Just Right. What Do You See? What Do You Think? Investigate.

Section 7. Laws of Thermodynamics: Too Hot, Too Cold, Just Right. What Do You See? What Do You Think? Investigate. Chapter 6 Electricity for Everyone Section 7 Laws of Thermodynamics: Too Hot, Too Cold, Just Right What Do You See? Learning Outcomes In this section, you will Assess experimentally the final temperature

More information

BASIC ELECTRONICS PROF. T.S. NATARAJAN DEPT OF PHYSICS IIT MADRAS LECTURE-4 SOME USEFUL LAWS IN BASIC ELECTRONICS

BASIC ELECTRONICS PROF. T.S. NATARAJAN DEPT OF PHYSICS IIT MADRAS LECTURE-4 SOME USEFUL LAWS IN BASIC ELECTRONICS BASIC ELECTRONICS PROF. T.S. NATARAJAN DEPT OF PHYSICS IIT MADRAS LECTURE-4 SOME USEFUL LAWS IN BASIC ELECTRONICS Hello everybody! In a series of lecture on basic electronics, learning by doing, we now

More information

Module P7.3 Internal energy, heat and energy transfer

Module P7.3 Internal energy, heat and energy transfer F L E X I B L E L E A R N I N G A P P R O A C H T O P H Y S I C S Module P7.3 Internal energy, heat and energy transfer 1 Opening items 1.1 Module introduction 1.2 Fast track questions 1.3 Ready to study?

More information

SAMPLE PAPER 1 XI PHYSICS

SAMPLE PAPER 1 XI PHYSICS SAMPLE PAPER 1 o A n XI PHYSICS Time: Three Hours Maximum Marks: 70 General Instructions (a) All questions are compulsory. (b) There are 30 questions in total. Questions 1 to 8 carry one mark each, questions

More information

14 Engineering physics

14 Engineering physics Option B 14 Engineering physics ESSENTIAL IDEAS The basic laws of mechanics have an extension when equivalent principles are applied to rotation. Actual objects have dimensions and they require an expansion

More information

Notes 5: More on regression and residuals ECO 231W - Undergraduate Econometrics

Notes 5: More on regression and residuals ECO 231W - Undergraduate Econometrics Notes 5: More on regression and residuals ECO 231W - Undergraduate Econometrics Prof. Carolina Caetano 1 Regression Method Let s review the method to calculate the regression line: 1. Find the point of

More information

THE IDEAL GAS LAW AND KINETIC THEORY

THE IDEAL GAS LAW AND KINETIC THEORY Chapter 14 he Ideal Gas Law and Kinetic heory Chapter 14 HE IDEAL GAS LAW AND KINEIC HEORY REIEW Kinetic molecular theory involves the study of matter, particularly gases, as very small particles in constant

More information

The Gas Laws. The effect of adding gas. 4 things. Pressure and the number of molecules are directly related. Page 1

The Gas Laws. The effect of adding gas. 4 things. Pressure and the number of molecules are directly related. Page 1 The Gas Laws Describe HOW gases behave. Can be predicted by the theory. The Kinetic Theory Amount of change can be calculated with mathematical equations. The effect of adding gas. When we blow up a balloon

More information

The final numerical answer given is correct but the math shown does not give that answer.

The final numerical answer given is correct but the math shown does not give that answer. Note added to Homework set 7: The solution to Problem 16 has an error in it. The specific heat of water is listed as c 1 J/g K but should be c 4.186 J/g K The final numerical answer given is correct but

More information

Instructor Now pick your pencils up and get this important equation in your notes.

Instructor Now pick your pencils up and get this important equation in your notes. Physics 605 Mechanical Energy (Read objectives on screen.) No, I haven t been playing with this toy the whole time you ve been gone, but it is kind of hypnotizing, isn t it? So where were we? Oh yes, we

More information

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 12 Steam Turbine - Impulse Good afternoon. We were studying

More information

Latent Heat Calculations

Latent Heat Calculations Latent Heat Calculations What heat quantities are needed to change a substance from a liquid to a gas? How much energy is needed to melt a solid to a liquid? Is it the same for each substance? Let s look

More information

Stirling heat engine Internal combustion engine (Otto cycle) Diesel engine Steam engine (Rankine cycle) Kitchen Refrigerator

Stirling heat engine Internal combustion engine (Otto cycle) Diesel engine Steam engine (Rankine cycle) Kitchen Refrigerator Lecture. Real eat Engines and refrigerators (Ch. ) Stirling heat engine Internal combustion engine (Otto cycle) Diesel engine Steam engine (Rankine cycle) Kitchen Refrigerator Carnot Cycle - is not very

More information

Density, Pressure and Change of State

Density, Pressure and Change of State Density, Pressure and Change of State Syllabus points: 5.1 use the following units: degrees Celsius ( o C), kelvin (K), joule (J), kilogram (kg), kilogram/metre 3 (kg/m 3 ), metre (m), metre 2 (m 2 ),

More information

Lesson 3. Measuring Volume

Lesson 3. Measuring Volume Math 5 Lesson 3 Measuring Volume Shipping Cars Each day cars are packed into containers and placed on large ships to be delivered to places all over the world. It is really important to get as many cars

More information